My creative writing teacher gave me a list of competitions, and one of them requires a protagonist that is transgender. What does it mean? Is it like Mulan, how she dressed up like and pretended to be a man, or does it mean people who have surgery to....you know...?

I am not certain "pretending" is an apt description. If a man is dressed up as a woman, he may not be "pretending", at least in his viewpoint.

Your teacher is giving you a very adult topic in which you probably do not have much experience with, I suggest you discuss this with your mom to get some adult thinking input. That probably will give you some greater insight for your writing point of view.